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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_935.54', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [-0.9238795325112867, -0.3826834323650898], 'a4': [2.9010907910729803e-30, -1.0], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9238795325112867, 0.3826834323650898], 'a7': [-0.3826834323650898, -0.9238795325112867], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 4.34212174533803, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [17, [1]]], 'bad_primes': [5, 11, 17], 'central_character': '935.54', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 935, 'conductor_radical': 935, 'conjugate': 'dirichlet_L_935.329', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^9', 'a^12', 0, 'a^7', 'a^11', 'a^10', 'a^2', 0, 0, 'a^5', 'a^4', 'a^9', 0, 'a^8', 0, 'a^0', 'a^6', 0, 'a^4', 0, 'a^7', 'a^3', 0, 'a^2', 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'191.92003639424649508254761339394', '192.62749524450631315549252753417', '193.37725413115189801925323695542', '193.74610122974140412729205163086', '194.470362695434202773064261965852', '194.68669236757061968068926676009', '195.44268280682178335681148834695', '196.02401398753721081344061465608', '196.38247688751514621109350693870', '197.40205811359480562600317719614', '197.817924409305620544387951362646', '198.73575207557516451554840960626', '199.56351722551229977918789738810'], 'prelabel': '1-935-935.54-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.34212174533803, 'root_angle': 0.30928116463685223, 'root_number': '0.563949729040615847990915398826+0.825809120266309462646928478906*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.154640582318', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.700897935782800503515922308636-0.427180646969863757910546470430*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32584295697', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.07886041126', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.62410689378', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.34212174533803, 'bad_primes': [5, 11, 17], 'central_character': '935.54', 'conductor': 935, 'conductor_radical': 935, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/935/54'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-935-935.54-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-935-935.54-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.34212174533803, 'root_angle': 0.15464058231842612, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32584295697', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_935.54', 'Lhash_array': ['dirichlet_L_935.54'], 'label': '1-935-935.54-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/935/54'}
Lfunction data - 1-935-935.54-r0-0-0